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Dividing Fractions: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Dividing FractionsDividing Fractions: Definition and ExampleTable of ContentsDefinition of Dividing Fractions

Dividing fractions refers to performing division operations where at least one fraction is involved. This can include dividing a fraction by another fraction (like 34÷12\frac{3}{4} \div \frac{1}{2}43​÷21​), dividing a whole number by a fraction (such as 7÷127 \div \frac{1}{2}7÷21​), or dividing a fraction by a whole number (like 34÷6\frac{3}{4} \div 643​÷6). When we divide fractions, we're essentially determining how many times one fraction fits into another, similar to how traditional division works with whole numbers. The result of dividing fractions can be either a fraction or a whole number.

Division of fractions follows several important properties that are consistent with whole number division. These properties include: when a fraction is divided by 1, the result is the fraction itself (34÷1=34\frac{3}{4} \div 1 = \frac{3}{4}43​÷1=43​); when zero is divided by a non-zero fraction, the result is always 0 (0÷34=00 \div \frac{3}{4} = 00÷43​=0); when a non-zero fraction is divided by itself, the result equals 1 (34÷34=1\frac{3}{4} \div \frac{3}{4} = 143​÷43​=1); and division by zero is undefined (34÷0\frac{3}{4} \div 043​÷0 is not defined).

Examples of Dividing Fractions Example 1: Dividing Simple Fractions Problem:

Divide 15÷110\frac{1}{5} \div \frac{1}{10}51​÷101​

Step-by-step solution: Step 1, remember the key rule for dividing fractions: Keep, Change, Flip. This means we keep the first fraction, change the division sign to multiplication, and flip (find the reciprocal of) the second fraction. Step 2, apply this rule to our problem: Keep 15\frac{1}{5}51​ as is Change ÷\div÷ to ×\times× Flip 110\frac{1}{10}101​ to get 101\frac{10}{1}110​ (or simply 10) Step 3, multiply the fractions: 15×101=1×105×1=105\frac{1}{5} \times \frac{10}{1} = \frac{1 \times 10}{5 \times 1} = \frac{10}{5}51​×110​=5×11×10​=510​ Step 4, simplify the result by dividing both numerator and denominator by their greatest common factor (5): 105=21=2\frac{10}{5} = \frac{2}{1} = 2510​=12​=2

Therefore, 15÷110=2\frac{1}{5} \div \frac{1}{10} = 251​÷101​=2, which means 15\frac{1}{5}51​ contains exactly 222 of 110\frac{1}{10}101​.

Example 2: Dividing a Mixed Number by a Fraction Problem:

Divide 123÷571\frac{2}{3} \div \frac{5}{7}132​÷75​

Step-by-step solution: Step 1, convert the mixed number to an improper fraction: 123=3×1+23=531\frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}132​=33×1+2​=35​ Step 2, apply the Keep, Change, Flip rule: Keep 53\frac{5}{3}35​ as is Change ÷\div÷ to ×\times× Flip 57\frac{5}{7}75​ to get 75\frac{7}{5}57​ Step 3, multiply the fractions: 53×75=5×73×5=3515=73\frac{5}{3} \times \frac{7}{5} = \frac{5 \times 7}{3 \times 5} = \frac{35}{15} = \frac{7}{3}35​×57​=3×55×7​=1535​=37​ Step 4, convert the improper fraction to a mixed number if desired: 73=213\frac{7}{3} = 2\frac{1}{3}37​=231​

Therefore, 123÷57=2131\frac{2}{3} \div \frac{5}{7} = 2\frac{1}{3}132​÷75​=231​.

Example 3: Solving a Word Problem with Fraction Division Problem:

Max is painting toy cars. He has 2142\frac{1}{4}241​ L of paint. If each car requires 38\frac{3}{8}83​ L of paint, how many cars can Max paint?

Step-by-step solution: Step 1, identify what we're looking for. We need to determine how many cars Max can paint, which means dividing the total amount of paint by the amount needed per car. Step 2, convert the mixed number to an improper fraction: 214=4×2+14=942\frac{1}{4} = \frac{4 \times 2 + 1}{4} = \frac{9}{4}241​=44×2+1​=49​ liters of paint Step 3, set up the division problem: Number of cars = 94÷38\frac{9}{4} \div \frac{3}{8}49​÷83​ Step 4, apply the Keep, Change, Flip rule: Keep 94\frac{9}{4}49​ as is Change ÷\div÷ to ×\times× Flip 38\frac{3}{8}83​ to get 83\frac{8}{3}38​ Step 5, calculate the result: 94×83=9×84×3=7212=6\frac{9}{4} \times \frac{8}{3} = \frac{9 \times 8}{4 \times 3} = \frac{72}{12} = 649​×38​=4×39×8​=1272​=6 Step 6, interpret the answer: Max can paint 666 toy cars with 2142\frac{1}{4}241​ liters of paint. Comments(5)MCMs. CarterSeptember 17, 2025This page was a lifesaver! The Keep, Change, Flip method was so clear—I used it to help my son with his homework, and he actually got it. Thanks for the step-by-step examples!

NNatureLover75September 10, 2025This page was a lifesaver! The step-by-step Keep, Change, Flip method made dividing fractions so easy for my kids. We even used the examples for extra practice, and they nailed their homework!

NNatureLover77August 27, 2025I’ve been struggling to explain dividing fractions to my son, but this page broke it down so clearly! The Keep, Change, Flip method was a game-changer for us. Thanks for the helpful examples!

MCMs. CarterAugust 20, 2025I used the 'Keep, Change, Flip' method explained here to help my daughter with her homework, and it finally clicked for her! The examples are super clear—thank you for making dividing fractions so easy to understand!

MMathMom25July 30, 2025I’ve used the glossary to teach my kids the Keep, Change, Flip method, and it made dividing fractions so much easier for them! They loved the step-by-step examples—super helpful resource.

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